Properties

Label 18.4.c
Level $18$
Weight $4$
Character orbit 18.c
Rep. character $\chi_{18}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 18.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(18, [\chi])\).

Total New Old
Modular forms 22 6 16
Cusp forms 14 6 8
Eisenstein series 8 0 8

Trace form

\( 6q + 2q^{2} + 3q^{3} - 12q^{4} + 18q^{5} - 18q^{6} + 12q^{7} - 16q^{8} - 105q^{9} + O(q^{10}) \) \( 6q + 2q^{2} + 3q^{3} - 12q^{4} + 18q^{5} - 18q^{6} + 12q^{7} - 16q^{8} - 105q^{9} + 39q^{11} + 24q^{12} - 24q^{13} + 100q^{14} + 90q^{15} - 48q^{16} - 78q^{17} + 156q^{18} + 210q^{19} + 72q^{20} - 36q^{21} - 18q^{22} - 264q^{23} - 24q^{24} - 219q^{25} - 392q^{26} - 96q^{28} - 348q^{29} - 288q^{30} - 6q^{31} + 32q^{32} + 765q^{33} + 90q^{34} + 1332q^{35} + 516q^{36} + 192q^{37} + 322q^{38} - 582q^{39} - 207q^{41} - 816q^{42} + 129q^{43} - 312q^{44} - 702q^{45} + 504q^{46} - 660q^{47} - 144q^{48} - 585q^{49} + 614q^{50} - 153q^{51} - 96q^{52} + 528q^{53} + 954q^{54} - 1404q^{55} + 400q^{56} + 987q^{57} + 252q^{58} - 327q^{59} - 936q^{60} + 858q^{61} - 1664q^{62} - 1794q^{63} + 384q^{64} + 414q^{65} + 288q^{66} + 1587q^{67} + 156q^{68} + 1494q^{69} + 216q^{70} - 312q^{71} - 24q^{72} - 258q^{73} + 856q^{74} + 3231q^{75} - 420q^{76} + 708q^{77} + 132q^{78} - 1482q^{79} - 576q^{80} + 315q^{81} - 2916q^{82} - 138q^{83} + 744q^{84} + 108q^{85} - 86q^{86} - 3204q^{87} - 72q^{88} - 3084q^{89} - 432q^{90} + 2508q^{91} - 1056q^{92} - 2634q^{93} + 612q^{94} - 2016q^{95} + 384q^{96} + 1029q^{97} + 2604q^{98} + 1152q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
18.4.c.a \(2\) \(1.062\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(9\) \(31\) \(q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
18.4.c.b \(4\) \(1.062\) \(\Q(\sqrt{-3}, \sqrt{-35})\) None \(4\) \(3\) \(9\) \(-19\) \(q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)